I am using the Kaplan LSAT premium prep book and I’ve gotten to the section in formal logic that discusses the “if not x then y” conditional statements.
I am struggling because it’s says…
If not x then y
If not y then x
Both x and y
… are all possibilities. How is both x and y together a possibility? It confuses me because it’s set up as if one exists the other can’t, so how is there possibility for all to exist together?
One example is:
If your students aren’t assigned the time-consuming War and Peace, they will be assigned both Anna Karenina and Resurrection.
I deduced it as…
If not WP then AK and R.
If not AK or not R then WP.
But the book shows that “WP and either AK or R” is possible and “WP and AK and R” being assigned is possible.
Can someone dumb this down as to how those last two answers are possible?
Thank you for help!
**Edit: here is the exact explanation from the book
“If NOT WP → AK AND R
If NOT AK OR NOT R → WP
OR
Either WP OR [AK AND R combo]
Note: Students could be assigned War and Peace and one of the other two books, or they could be assigned all three. The triggers in the original statement and its contrapositive are all negative statements, so there's no way to determine what happens if they are assigned one or more of these books.
Another helpful way to translate this statement would be to break it down into smaller pieces:
If not WP → AK
If not AK → WP
If not WP → R
If not R → WP
Notice how that translation covers all of the triggers and results in the statement”